Subalgebras of Sheffer Stroke BCK-Algebras Illuminated by the New Fuzzy Set Environment

Tahsin Oner, Young Bae Jun () and Ibrahim Senturk ()
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Tahsin Oner: Department of Mathematics, Faculty of Science, Ege University, Izmir, 35100, Turkey
Young Bae Jun: Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea
Ibrahim Senturk: Department of Mathematics, Faculty of Science, Ege University, Izmir, 35100, Turkey

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 02, 541-556

Abstract: For the purpose of dealing with the subalgebras of Sheer stroke BCK-algebras associated with the YJϱ-fuzzy set, the concept of YJϱ-fuzzy subalgebras in Sheffer stroke BCK-algebras is introduced and the properties involved are investigated. Conditions for creating a YJϱ fuzzy subalgebra from a given fuzzy are explored. The relationship between fuzzy subalgebra and the YJϱ fuzzy subalgebra is discussed, and conditions are given for the YJϱ-fuzzy subalgebra to be a fuzzy subalgebra. The task of creating a new YJϱ-fuzzy subalgebra is established using the given fuzzy subalgebra. Two types of level sets are created and the conditions under which they become subalgebras are explored.

Keywords: Sheffer stroke BCK-algebra; (fuzzy) subalgebra; YJϱ-fuzzy subalgebra (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500243

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